Bring NCTM Standards to Life: Best Practices, High School

 

Yvelyne Germain- Mc Carthy 

Eye on Education | 1998 | 206 páginas | rar -pdf | 8 Mb

link (password: matav)

By presenting teacher profiles and sample lessons from across the country, this book shows that the NCTM standards reflect successful practices of teachers at the "grass roots".

Contents

ACKNOWLEDGMENTS.  ix

ABOUT THE AUTHOR. . x

FOREWORD.  xi

REFLECTIONS FROM THE FIELD . xii

1 INTRODUCING THE NCTM REFORM DOCUMENTS. 1

This Book's Purpose.2

Introducing the NCTM Reform Documents  3

Constructivism.. 3

Skills for Citizens of the Twenty-First Century . 5

The Curriculum and Evaluation Standards for School Mathematics . 9

The Curriculum Standards for Middle and High School ....... 10

Common Standards for the Middle Grades and High School. . . . 11

Additional High School Standards . 12

Learning, Teaching, and Assessment.  . 14

The Professional Standards for Teaching Mathematics 14

The Assessment Standards.  . 15

Principles and Standards for School Mathematics .16

National Board Certification . 17

2 EXEMPLARY PRACTICE: WHAT DOES IT LOOK LIKE?. 19

Traditional Teachers in Transition . 19

Envisioning Reform-Based Classrooms 24

3 BEN PREDDY: INTEGRATING MATHEMATICS  27

4 YVONNE STALLINGS: INVESTING FOR A FOUR-YEAR COLLEGE EDUCATION.  39

5 CYNTHIA SUTHERLIN: MATHEMATICAL MODELING OF LINEAR FUNCTIONS IN THE SCIENCES  59

6 DON CROSSFIELD: MARCHING FROM ALGEBRA TO TRIGONOMETRY AND BEYOND 73

7 VIRGINIA HIGHSTONE: EQUATIONS THAT MODEL GROWTH AND DECAY.. 87

8 HENRY KRANENDONK: RAISIN GEOMETRY- EXPLORING THE BALANCE POINT AND ITS APPLICATIONS  103

9 MURRAY SIEGEL: DISCOVERING THE CENTRAL LIMIT THEOREM  119

10 CLAUDIA CARTER: How A RUMOR SPREADS-AN INTRODUCTION TO LOGISTIC CURVES 133

11 KATHRYN HILL: CONNECTING INFORMAL PROOFS TO FORMAL PROOFS WITH A GEOBOARD. 143

12 MICHAEL LEHMAN: GROUP PERFORMANCE ASSESSMENTS ... 157

13 LEARNING CENTERS OF THE TWENTY-FIRST CENTURY . 175

Revisiting Questions. . . 176

Can It Be True that All Students Can Do Mathematics? 176

Can All Students Do Algebra? 177

Curriculum Concerns of a Parent. . .

What Can Classroom Teachers Do? 181

What Can Administrators Do? . . 181

What Can Teacher Educators Do? 183

What Can We All Do Together? . 184

Conclusion.  . 184

REFERENCES . 187

Numeracy and Mathematics Across the Primary Curriculum: Building Confidence and Understanding

 David Coles e Tim Copeland

David Fulton Publishers | 2002 | 113 páginas | rar - pdf | 18,3Mb

link (password: matav)

The key to good primary teaching of numeracy and mathematics is confidence in mathematical knowledge and its relevance to the real world. In particular, effective implementation of the National Numeracy Strategy requires student teachers, primary teachers and mathematics coordinators to realize the place of mathematics across the range of National Curriculum subjects. 
This book explores mathematics as a set of tools for thinking about, designing, evaluating and changing the world of the child through the broader curriculum, rather than focusing on skills and concept building exclusively in the 'mathematical world.' Practical activities are included to stimulate readers to apply these ideas with confidence both within and beyond the mathematics lesson.

Contents
Acknowledgements iv
Introduction 1
1 Science: Quantifying the world 15
2 History: Mathematics and evidence from the past 25
3 Geography: A place for number 35
4 English: Patterns of language and patterns in language 43
5 Physical Education: Building geometrical thinking into playing games 56
6 Music: Notes and number 69
7 Design and Technology: Creating with numbers 80
8 Art: Keeping things in proportion 96
References 106
Index 107

Primary Teaching Assistants: Curriculum in Context

Carrie Cable

Routledge | 2005 | 254 páginas | rar - pdf | Mb

link (password: matav)

Teaching assistants are uniquely placed to support children’s involvement with learning through the curriculum. This book explores those issues that are central to that process. Specifically it examines:

• strategies for supporting learning and assessment in English, maths and science
• inclusive and imaginative practices in all areas of learning
• home and community contexts for learning
• working practices which support professional development.

This book is written primarily for learning support staff, their teaching colleagues and those responsible for professional development and training.

Contents

Acknowledgements

Introduction

Carrie Cable and Ian Eyres

Section 1: Children and the curriculum

Introduction to Section 1

Carrie Cable and Ian Eyres

1 Play

Stephanie Northen

2 Talk about texts at the computer: using ICT to develop children’s oral and literate abilities

Neil Mercer, Manuel F ernandez, Lyn Dawes, Rupert Wegerif and Claire Sams

3 ICT, learning and primary mathematics

John Ralston

4 Reflections on six years of the National Literacy Strategy

Kathy Hall

5 What can teachers learn from the language that children use?

Chris Bills

6 Watching and learning: the tools of assessment

Cathy Nutbrown

7 Social constructivism in the classroom

Judith Watson

8 Constructivism and primary science

Patricia Murphy

9 Supporting science in Key Stage 1

Janet K ay

10 Learning science

Joan Solomon with Stephen Lunn

Section 2: Contexts for learning

Introduction to Section 2

Carrie Cable and Ian Eyres

11 Learning at Coombes School 83

Bob Jeffrey and Peter Woods

12 Making sense of it all: using ICT to support older bilingual new arrivals 93

Sheilagh Crowther with Ian Eyres

13 A well-equipped hamster cage: the rationalisation of primary school playtime 96

Sarah Thomson

14 The articulate playground: trainee teachers meet pocket monsters 104

Elizabeth Grugeon

15 School buildings: ‘A safe haven, not a prison . . 1 1 0

Catherine Burke and Ian Grosvenor

16 Joining Gabriel’s play 116

Kayte Brim acom be with Roger Hancock

17 The role of grandparents in children’s learning 120

Charmian Kenner, Tahera Arju, Eve Gregory, John Jessel and Mahera Ruby

18 Supplementary schools and their parents: an overlooked resource? 127

John  Bastiani

Section 3: Working together 131

Introduction to Section 3

Carrie Cable and Ian Eyres

19 Winning teams 133

Hilary Cremin, Gary Thomas and Karen Vincett

20 Supporting primary mathematics 136

Jenny Houssart

21 Reflections on practice: three bilingual teaching assistants/instructors reflect on their roles 143

Carrie Cable

22 Enabling children’s creativity 151

Lindsey Haynes with Anna Craft
23 ‘Are they teaching?’ An alternative perspective on parents as educators
Janet Atkin and John Bastiani
24 Effective home-school links
Suzanne Brown
25 Developing pupils’ skills in self-assessment in the primary classroom
Ruth Dann
Section 4: Perspectives and voices
Introduction to Section 4
Carrie Cable and Ian Eyres
26 ‘Whoops, I forgot David’: children’s perceptions of the adults
who work in their classrooms
Ian Eyres, Carrie Cable, Roger Hancock and Janet Turner
27 What do pupils and parents think?
Patricia Atkinson
28 Getting your voice heard and making a difference
Chris Scrivener
29 Bangladeshi women and their children’s reading
Adrian Blackledge
30 Social outcasts
Times Educational Supplement
31 Common sense has much to learn from moonshine
Philip Pullman
32 Beyond the tests: literacy in successful schools
Thelma Hall with Ian Eyres
33 Co-ordinating support for learning
Liz Gerschel
34 Learning through the enriched curriculum
Dympna Meikleham with Roger Hancock
Index

Where's the Wonder in Elementary Math?: Encouraging Mathematical Reasoning in the Classroom

Judith McVarish

Routledge | 2007 | páginas | rar - pdf | Mb

link (password: matav)

This book argues that even in today's high-stakes testing environment, 'teaching to the test' need not be teachers’ only focus as they introduce young children to mathematics. Judith McVarish demonstrates how building a community of learners and using problem solving to engage students can help teachers encourage students’ disposition to creative thinking and reasoning—skills that can otherwise become lost due to the pressure of the many other expectations placed upon both teachers and students. This book offers strategies for infusing mathematics learning and reasoning into elementary school classrooms while meeting curriculum and testing mandates. The teacher researcher component of each chapter provides a vehicle for teachers to bring their own expertise and questions back into the teaching and learning equation.

Contents
Acknowledgments ix
Series Editor’s Foreword xi
Chapter 1 Setting the Stage . 1
Chapter 2 What Does the Room Teach? 25
Chapter 3 Who Asks the Questions? Who Answers Them? 43
Chapter 4 How Can I Tune Transitions to a New Key? 65
Chapter 5 What Is Real about Homework? . 79
Chapter 6 How Do I De-Fang the Test? . 99
Chapter 7 How Can We Take Critical Thinking Beyond the Classroom? 119
Chapter 8 What Do Parents Know? . 139
Chapter 9 Is Thinking about Thinking Just a Play on Words? . 155
References  173

Index 177

The Really Useful Maths Book: A Guide to Interactive Teaching

Tony Brown e Henry Liebling 

Routledge | 2014 - 2ª edição | 326 páginas | rar - pdf | Mb

link (password: matav)

1ª edição - 2005

The Really Useful Maths Book is for all those who want children to enjoy the challenge of learning mathematics. With suggestions about the best ways to use resources and equipment to support learning, it describes in detail how to make learning the easy option for children.An easy-to-follow, comprehensive guide packed with ideas and activities, it is the perfect tool to help teachers who wish to develop their teaching strategies.

The second edition has been fully updated in light of the latest research, as well as in response to the new mathematics curriculum. It includes many more practical activities for each mathematical topic and explores exciting new areas. Key topics covered include:

• Numbers and the number system
• Operations and calculations
• Shape and space
• Measures, statistics and data handling
• Cross-curricular approaches
• Resources and planning for teaching and learning
• Contexts for making sense of mathematics
• Bridges, strategies and personal qualities
• Dialogue and interactive teaching
• International perspectives on teaching and learning
• Psychology and neuroscience to maximize learning.

The Really Useful Maths Book makes mathematics meaningful, challenging and interesting. It will be invaluable to practicing primary teachers, subject specialists, maths co-ordinators, student teachers, mentors, tutors, home educators and others interested in mathematics education programmes.

Contents

List of resource pages viii

Acknowledgements ix

Why another book about primary school mathematics? x

Using The Really Useful Maths Book xiv

PART I MATHEMATICAL ACTIVITIES AND TEACHING

STRATEGIES 1

Introduction 3

N NUMBERS AND THE NUMBER SYSTEM 10

1 Counting and counting out 10

2 Saying and making numbers 16

3 Arabic and other number systems 26

4 Working with grids 32

5 Working with target boards 40

6 Working with sets 46

7 Working with square numbers 48

8 Exploring algebra 50

9 Taking ideas from ‘floor to head’ 58

O OPERATIONS AND CALCULATIONS 64

1 Number lines 64

2 The story of 24 68

3 Arithmetic operations 76

4 Arithmogons and other puzzles 88

5 Teaching multiplication tables 100

6 Divisibility rules 110

S SHAPE AND SPACE 114

1 Visualisation techniques and activities 114

2 Activities and investigations 120

3 Working with cloths 128

4 Unusual and unfamiliar 134

5 Changing shapes 140

M MEASURES, STATISTICS AND DATA HANDLING 146

1 Measures and measurement 146

2 Data handling and using the media 156

3 Statistics and probability 160

4 Using personal measurement 166

5 Investigating measurement 168

X CROSS-CURRICULAR APPROACHES 179

1 Cross-curricular approaches 179

2 Playing with the language of mathematics 184

3 Maths in music, dance and knitting 188

4 Maths, sustainability and the global dimension 193

5 Reasoning, logic, proof and programming 197

PART II DEVELOPING INTERACTIVE TEACHING

STRATEGIES 203

Introduction 204

A TEACHING AND LEARNING FROM INTERNATIONAL PERSPECTIVES 205

1 Policy and content 205

2 Pupil performance 207

3 Classroom practice 209

4 Findings from psychology and neuroscience 212

B CHILDREN AND TEACHERS INTERACTING 218

1 Pupil, teacher, mathematics: a dynamic model of interaction 218

2 Interactive teaching 220

3 Children talking, teachers listening 221

4 Questions and questioning 224

5 Assessment for learning 232

C RESOURCES AND PLANNING FOR TEACHING AND LEARNING 245

1 Achieving balance in the mathematics curriculum 245

2 Using resources to emphasise mathematical attributes 247

3 Resources for counting and calculation 251

4 Planning to optimise learning 254

D CONTEXTS FOR MAKING SENSE OF MATHEMATICS 261

1 Using different contexts to help make sense of mathematics 261

2 Practical activities and solving problems 264

E BRIDGES, STRATEGIES AND PERSONAL QUALITIES 268

1 Building bridges for learning 268

2 The importance of strategy building 272

3 Eight qualities of successful learners 277

PART III ADDITIONAL MATERIAL 281

How to use Part III, QR codes, the companion website and glossary 282

Additional sources 283

Bibliography 287

Journals, organisations, software, equipment and other resources 290

Websites 293

Author index 299

Pedagogical issues index 300

Maths content index 304

Activity matrix 306

Common Core Mathematics in a PLC at Work, Grades 6-8

Diane J. Briars, Harold Asturias, David Foster e Mardi A. Gale

Solution Tree | 2012 | páginas | rar - epub | Mb

link (password: matav)

This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for grades 6-8. Discover what students should learn and how they should learn it at each grade level. Acquire strategies for meeting the rigor of the grades 6-8 standards, including the unique content around ratios, proportions, and relationships at grades 6 and 7. Get insight into the new expectations for grades 6-8 assessment as well as the readiness required for the high school standards.

Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You'll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students.

Benefits

- Discover the five essential paradigm shifts necessary to implement the CCSS for mathematics.

- Receive guidance on forming and sustaining collaborative teams in a Professional Learning Community at Work culture.
- Develop a 'less is more'; content mind-set: fewer standards will result in the opportunity of time needed for deeper rigor and conceptual understanding work with students.
- Gain helpful formative assessment strategies for development of student proficiency in the Standards for Mathematical Practice.
- Access dozens of tools, activities, examples, resources, and reproducibles to help teachers and teams analyze, interpret, and implement the common core standard expectations for instruction and assessment.
- Examine the research-affirmed foundation of mathematics content and process standards from 1989 to 2010 and deepen your understanding of the common core expectations.

Contents
1. Using high-performing collaborative teams for mathematics
2. Implementing the common core standards for mathematical practice
3. Implementing the common core mathematics content in your curriculum
4. Implementing the teaching-assessing-learning cycle
5. Implementing required response to intervention
Epilogue. Your mathematics professional development model
Appendix A. Standards for mathematical practice
Appendix B. Standards for mathematical content, grade 6
Appendix C. Standards for mathematical content, grade 7
Appendix D. Standards for mathematical content, grade 8.

The Math Teacher’s Toolbox How to Teach Math to Teenagers and Survive

Nicholas J. Rinaldi 

R&L Education | 2013 | 145 páginas | rar - pdf | 1,4 Mb

link (password : matav)

Whether you are a new or an experienced math teacher, The Math Teachers’ Tool Box provides guidance and serves as a reference book of topics, ideas, and resources. This book provides teachers with various tools to improve their classroom management skills, to actively involve students in lessons, and as a result, raise their interest level and improve learning. The ideas presented have been classroom-tested over many years and can be used in virtually any middle or high school classroom.

ContentsPreface v
Acknowledgements ix
Introduction xi
1 On Your Marks, Get Set: Establishing Expectations 1
2 Put Me In, Coach: Getting Students Actively Involved 11
3 Ladies and Gentlemen, Start Your Engines: Opening-of-Class Activities 13
4 And the Children Shall Lead: Rinaldi’s Routine—Creating a Student-Centered Classroom 19
5 Eureka: Inquiry-Based and Discovery Lessons 29
6 “When Will I Ever Use This?”: Problems in the Students’ World 43
7 He Who Laughs, Lasts: Humor in the Classroom 55
8 Calculate This!: Using the Graphing Calculator 61
9 The Pen Is Mightier Than the Calculator: Writing and Reading in a Math Class 71
10 It’s Game Time: Classroom Competitions 75
11 All Good Things Must Come to an End: Closing Activities 91
12 But Wait . . . There’s More! 93
Conclusion 109
Appendix 111

Teaching Statistics and Probability

(Yearbook - National Council of Teachers of Mathematics)
Albert P. Shulte e James R. Smart

National Council of Teachers of Mathematics | 1981 | 258 páginas | rar - pdf | 7,22 Mb

link (password : matav)

This 1981 yearbook of the National Council of Teachers of Mathematics (NCTM) offers classroom ideas for teaching statistics and probability, viewed as important topics in the school mathematics curriculum. Statistics and probability are seen as appropriate because they: (1) provide meaningful applications of mathematics at all levels; (2) provide methods for dealing with uncertainty; (3) give us some understanding of the statistical arguments, good and bad, with which we are continually bombarded; (4) help consumers distinguish sound use of statistical procedures for unsound or deceptive uses; and (5) are inherently interesting, exciting, and motivating topics for most students. The text is divided into eight parts, labeled: (1) The Case for Teaching Statistics and Probability; (2) Samples of Existing Courses or Programs; (3) Classroom Activities; (4) Teaching and Learning Specific Topics; (5) Applications; (6) Statistical Inference; (7) Monte Carlo Techniques and Simulation; and (8) Using Computers. The yearbook concludes with a bibliography and a list of suggested class projects

Creativity for a New Curriculum: 5-11

Lynn D Newton

Routledge | 2012 |  153 páginas | rar - pdf | 621 kb

link (password: matav)

Creativity for a New Curriculum: 5-11 provides an account of what creativity really means in the context of children’s learning in the primary school, and describes in practical terms what teachers can do to foster it. At a time of curriculum development and change, it focuses on the opportunity to build a new curriculum that is inclusive of creativity and is fit for the twenty-first century.

The value of fostering creative thinking and problem solving abilities in education is widely recognised for its capacity to confer an independence and ability to function effectively in life. As such, encouraging children to be creative thinkers and problem solvers should be an integral part of everyday teaching and learning across all subjects.

Building upon the research and practices of a group of educators studying creativity across the curriculum and coordinated by the author, this book provides primary teachers and trainee teachers with easy to understand explanations of what creativity means in the context of the subjects of the curriculum for young children. It introduces ideas for how to nurture and support it, and explores issues associated with fostering it, such as assessment. Chapters cover areas including:

• A brief history of creativity and pedagogy, including common misconceptions

• Strategies for creative learning as well as creative teaching

• Creativity in English

• Creativity in Mathematics

• Creativity in Science and Design and Technology

• Creativity in Art and Music

• Creativity in History and the Humanities

• Creativity in ICT

• International perspectives on creativity

Creativity for a New Curriculum: 5-11 is an ideal source of information for teachers, teacher trainers, students on teaching programmes and anyone interested in developing opportunities for creativity across the primary school curriculum.

Contents

About the Contributors vi

Introduction 1

Lynn Newton

1 Creativity and Problem Solving: An Overview 7

Douglas Newton

2 Creativity in English 19

Lynn Newton and David Waugh

3 Creativity in Mathematics 36

David Bolden

4 Creativity in Science and Design and Technology 48

Lynn Newton

5 Creativity in Art and Music 62

Douglas Newton, Hazel Donkin, Dimitra Kokotsaki and Lynn Newton

6 Creativity in History and the Humanities 80

Anthony Blake and Gail Edwards

7 Exploring Creativity within ICT: Concepts, Themes and Practices 94

Caroline Walker and Alan Gleaves

8 Recognizing Creativity 108

Douglas Newton

9 ‘Creativity is Our Hope’: A Wider Perspective on Creativity 120

Sophie Ward and Lynn Newton

10 Teaching for Creative Learning 131

Lynn Newton

Index 140

Mathematics in the Primary School A sense of progression

Sandy Pepperell, Christine Hopkins, Sue Gifford e Peter Tallant 

Routledge | 2009 - 3ª edição |190 páginas | rar - pdf | 3,95 Mb

link (password : matav)

• The role of talk in learning maths

• Teacher questioning

• Development of children’s reasoning

• Creative engagement with maths

• Assessment for learning and self assessment

• Suggested resources for teachers including ICT

Now in its third edition, Mathematics in the Primary School has been updated to reflect recent mathematics curriculum documentation and revised standards for QTS.

Key areas include:

Providing a coherent set of principles for teaching primary mathematics across the main topics in the curriculum, the authors explore children’s understanding of key areas of mathematics, at reception, infant and junior levels. Important principles and teaching approaches are identified, including the use of calculators and computers, and there is an emphasis on mental mathematics and problem solving supporting key issues raised by the Williams review (2008). Case studies are used throughout to illustrate how different teaching approaches are put into practice and how children respond to them, and there is advice on planning, organisation and assessment of mathematical learning in the classroom.

Emphasising the importance of teachers’ own mathematical knowledge and offering clear guidance and practical advice, this book is essential reading for students, NQTs and practising teachers with a focus on primary mathematics.

Contents

Acknowledgements viii

Preface to the third edition ix

Section 1: Using and applying mathematics 1

Mathematical thinking 1

1.1 Why do children learn mathematics in school? 1

Key questions 3

Case studies

How can we develop reasoning at Key Stage 1? 4

How can we develop reasoning at Key Stage 2? 5

Glossary 8

Section 2: Number 10

2.1 Introduction – the teaching of number 10

2.2 Number in the early years 10

Learning to count 11

What activities help children to count and learn about numbers and numerals? 13

Case studies

A nursery shopping game 14

Revised version of the game 17

Extensions 17

Starting to calculate 17

Some activities 19

Board games 23

2.3 Developing a feel for number 23

Understanding place value 24

Mental mathematics 26

Multiplication and division 27

Common misconceptions 29

Case study

Circle game 31

A range of methods for calculating 34

Fractions, decimals, percentages and division 42

Estimation 46

2.4 Extending the number system 46

Really large numbers 46

Glossary 48

Introducing negative numbers 49

Glossary 49

Fractions, decimals and percentages, ratio and proportion 50

Properties of numbers 55

Glossary 57

2.5 Ideas leading to algebra 58

Early generalisations: the search for pattern 58

Developing pattern and generalisation 58

Case study

Growing shapes 58

Seeing the link with algebra 60

Other activities leading to algebra 61

2.6 Solving numerical problems 62

Practical tasks 62

Real life problems 62

Problems within mathematics itself 63

Case study

How many ways can you make ... 48? 66

Assessment 67

Glossary 68

Solving equations 68

Section 3: Shape, space and measure 69

3.1 Shape and space: introduction 69

Teaching points 70

Case study

Visualising: an initial assessment activity 71

Visualising activities 72

3.2 Shape and space activities 72

Glossary 88

3.3 Measurement: general principles 91

Introduction 91

Standard and non-standard measures 92

Use and interpretation of measuring tools 95

Estimating 95

Assessing for starting points 96

3.4 Aspects of measurement 97

Length 97

Capacity and volume 98

Area 99

Perimeter 100

Weight and mass 100

Measuring time 102

Case study

Food technology 103

Organising the classroom and children appropriately 111

Solving problems involving measure 111

Glossary 112

Section 4: Handling data 113

4.1 Introduction 113

Handling data in the classroom 113

The data handling process 114

The teacher’s role in the process 115

4.2 Case studies

Case study at the Foundation Stage 123

Case study at Key Stage 2 126

4.3 Mathematical thinking and data handling 131

Solving problems 131

Mathematical communication 132

Reasoning mathematically 132

The use of computer databases 132

Key points to remember when children are using the computer 137

Activities 137

Examples for Foundation Stage/Key Stage 1 138

Examples for Key Stage 2 139

4.4 Probability 139

Probability in society 139

Activities 140

Glossary 142

Section 5: Planning, assessment and classroom organisation 148

5.1 Planning and assessment 148

Early years settings 148

Planning and assessment 149

Identify the learning objectives 150

Recording assessments 152

Reporting 154

5.2 Classroom organisation 154

Atmosphere and ethos 154

Starting an activity in stimulating ways 155

Encouraging and facilitating talk about mathematics 158

Groupings 162

Selecting and organising resources 164

Early years settings 164

Key Stages 1 and 2 165

5.3 Children with specific mathematics learning difficulties 167

Case studies

Two children with mathematical learning difficulties: Ben and Amanda 170

Conclusion 171

Resources 172

References 174

Index 176

Mathematics miseducation : the case against a tired tradition

Derek Stolp

ScarecrowEducation | 2005 | 208 páginas | rar - pdf | 17,76 Mb

link (password : matav)

Author and veteran teacher Derek Stolp has come to the conclusion that learning mathematics is of no real consequence for the vast majority of our children. This stance flies in the face of the conventional wisdom held among political leaders, business people, teachers, and parents that mathematics is an essential subject for all children to study well into their high school years. In Mathematics Miseducation, Stolp argues that mathematics, as currently taught, does not justify inclusion in the curriculum and he suggests practical changes that can be implemented within a traditional school environment to resuscitate mathematics education. In this book, the author demonstrates that our beliefs about what children need and what motivates them to learn promote practices that are counterproductive, and that these practices ultimately corrupt students' own healthy motivations. Stolp contends that there is too much emphasis upon academics in our schools, and that other important dimensions of education, such as the social, emotional, and moral development of our children, are ignored. Includes: * Progressive and practical alternatives to the traditional methods of teaching * Research and examples citing ways of bringing the discipline to life In seamlessly weaving theory and practice, Derek Stolp provides a narrative that is accessible to any adult concerned about what our children are learning in mathematics.

CONTENTSAcknowledgments
Introduction
PART I THE TRADITIONAL MODEL
Why Do I Need to Know This? The Case Against Traditional Mathematics
2 Whose Knowledge Is It? Experience in the Construction of Knowledge
3 So What's the Alternative? A New Model for Teaching Mathematics
PART II BEYOND THE TRADITION:
A PROGRESSIVE MODEL
4 Why Should I Care About This Stuff? Interest and Autonomy 85
5 How Do We Get These Kids to Learn? The Motivations of Children
6 Academics-Is That All We Should Care About? The Overlooked Intelligences 125
7 So What's the Alternative? A New Model for Teaching 141
8 Who Gets to Choose? Democratic Learning Communities 157
Appendix A: Mathematics Teacher 173
Appendix B: Exercises 177
References 181
Index 189
About the Author 193

A guide to mathematics leadership: sequencing instructional change

Don S. Balka, Ted H. (Henry) Hull e Ruth Ella Harbin Miles

Corwin | 2009 | 177 páginas | rar - pdf | 972 kb

link (password: matav)

Written by three noted mathematics educators, this volume presents a process-based approach to building a high-quality mathematics program based on five NCTM principles and four NCSM leadership principles.
Contents
List of Figures vii
Preface viii
Acknowledgments xvi
About the Authors xviii
PART I: PREPARING THE FOUNDATION 1
1. Understanding and Clarifying Leadership in Mathematics 2
What Is Leadership and Who Is a Leader? 4
Building a Culture of Success 5
NCTM Principles and NCSM Leadership Principles 6
2. Engaging and Empowering Staff 12
Staff Inclusion and Effective Communication 13
Leadership Decision Making 15
Instructional Leadership 16
Dynamics of Engagement and Empowerment 19
Expectations and Challenges 24
PART II: A LEADERSHIP MODEL 25
3. Articulating the Curriculum 26
Curriculum Alignment 27
Opportunity to Learn 30
Scope, Sequence, and Timeline Alignment 34
Rigorous Curriculum 38
4. Implementing the Curriculum 45
Curriculum Implementation 46
Monitored Implementation 47
Monitored Progress 56
5. Incorporating Effective Instructional Strategies 64
Incorporating Effective Instructional Strategies for All 65
Student Collaboration in the Form of Teamwork 66
Using Group-Worthy Problems 72
Incorporating Instructional Strategies for ELL Students 76
Matching Materials to Desired Instructional Strategies 84
Using Data to Inform Practice 1: Analyzing Student Work 86
Using Data to Inform Practice 2: Analyzing
Student Assessments 89
6. Providing Timely and Targeted Feedback 93
Using Pertinent Data 94
Targeted Information 98
Building Trust 104
7. Establishing Professional Learning Communities 108
Establishing Collaboration 109
Building Community 111
Facilitating Reflection 115
8. Fostering Professional Development 118
Structuring Effective Professional Development 119
Mentoring and Coaching 122
Other Approaches to Professional Development 124
PART III: CONTINUING THE WORK 127
9. Reflecting on How Students Learn Mathematics 128
What Mathematics Must or Should Students Learn? 129
What Methods and Tools Will Be Most Effective in Helping Students Learn? 129
What Does Research Say? 131
How Do Students Learn to Become Problem Solvers? 133
How Do Students Learn to Communicate Mathematics? 135
10. Putting It All Together 137
Looping, or Recycling, Through the Developmental Stages 138
Mathematics Leaders’ Influence 139
Guiding Questions for Critiquing the Developmental Stages 140
References 143
Index 149

Topics in Mathematics for Elementary Teachers: A Technology-Enhanced Experiential Approach

Sergei Abramovich 

Information Age Publishing | 2010 | 263 páginas | rar - pdf | 2,7 Mb

link (password: matav)

This book reflects the author's experience in teaching a mathematics content course for pre-service elementary teachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciences for the preparation of teachers demonstrating how abstract mathematical concepts can be motivated by concrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachers to grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts on higher levels of abstraction. A strong experiential component of the book made possible by the use of manipulative materials and digital technology such as spreadsheets, The Geometer's Sketchpad, Graphing Calculator 3.5 (produced by Pacific Tech), and Kid Pix Studio Deluxe makes it possible to balance informal and formal approaches to mathematics, allowing the teachers to learn how the two approaches complement each other. Classroom observations of the teachers' learning mathematics as a combination of theory and experiment confirm that this approach elevates one's mathematical understanding to a higher ground. The book not only shows the importance of mathematics content knowledge for teachers but better still, how this knowledge can be gradually developed in the context of exploring grade-appropriate activities and tasks and using computational and manipulative environments to support these explorations. Most of the chapters are motivated by a problem/activity typically found in the elementary mathematics curricula and/or standards (either National or New York State - the context in which the author prepares teachers). By exploring such problems in depth, the teachers can learn fundamental mathematical concepts and ideas hidden within a seemingly mundane problem/activity. The need to have experience in going beyond traditional expectations for learning is due to the constructivist orientation of contemporary mathematics pedagogy that encourages students to ask questions about mathematics they study. Each chapter includes an activity set that can be used for the development of the variety of assignments for the teachers. The material included in the book is original in terms of the approach used to teach mathematics to the teachers and it is based on a number of journal articles published by the author in the United States and elsewhere. Mathematics educators who are interested in integrating hands-on activities and digital technology into the teaching of mathematics will find this book useful. Mathematicians who teach mathematics to the teachers as part of their teaching load will be interested in the material included in the book as it connects childhood mathematics content and mathematics for the teachers.

Contents
Preface........ vii
1 Partition of Whole Numbers: Reasoning with Manipulatives and Computational Experiments.... 1
2 Combinatorial Models: From Trial and Error to Theory...... 21
3 Early Algebra with Kid Pix...... 39
4 Hidden Mathematics of the Multiplication Table..... 51
5 Application of Unit Fractions to Tesselations....... 69
6 Divisibility and Prime Numbers...... 91
7 Fibonacci Numbers and the Golden Ratio...... 113
8 From Arithmetic Sequences to Polygonal Numbers..... 135
9 The Multiplication Table Revisited....... 159
10 Proof and Proving............. 171
11 Computational Problem-Solving and Modeling......... 195
12 Numbers and Operations in Different Bases...... 211
13 Programming Details..... 231
References........... 245
Appendix: Some Useful Formulas..... 249

Outro livro do mesmo autor:

Computer-enabled mathematics : integrating experiment and theory in teacher education por Sergei Abramovich Idioma: Inglês   Editora: Hauppauge, N.Y. : Nova Science Publishers, ©2011.